BEGIN:VCALENDAR PRODID:-//eluceo/ical//2.0/EN VERSION:2.0 CALSCALE:GREGORIAN BEGIN:VEVENT UID:e6b49698eff545ae8392257cdee49235 DTSTAMP:20260505T221238Z SUMMARY:Conference in honour of Dr Martin Clark DESCRIPTION:This event is held in honour of Dr Martin Clark who passed away in 2025.  Colleagues\, friends and former students paid their own tribut es to him via  A tribute to Martin Clark 1938 – 2025\nParticipants are asked to register for the catering purposes. There is NO registration fee. \nRegistration deadline: 12 May 2026\nRegistration link\nPreliminary Progr amme\nDay 1\n·        09:00–9:15 Registration\, coffee\n·         09:15–9:30 Welcoming remark\n·        9:30–11:00 t wo talks\n·        11:00–11:30 Coffee\n·        11:30-1 3.00 two talks\n·        13:00–14:00 Lunch\n·        1 4:00–15:30 two talks\n·        15:30–16:00 Coffee\n·         16:00–17:30 two talks\n·        17:30-18:00 Remembering Martin\nDay 2\n·        09:00–10.30 two talks\n·        10:30–11.00 Coffee\n·        11:00–12.30 two talks\n·         13:00–14:00 Lunch \nList of speakers and talks\nSpeaker: Rich ard Vinter\nTitle: Clark’s Shifted Rayleigh Filter and Other Adventures in Applied Stochastic Analysis\nAbstract: Martin Clark is best known among researchers for his foundational work on stochastic processes\, nonlinear filtering and stochastic control. But his deep knowledge of stochastic an alysis was allied with practical interests\, leading to important contribu tions to signal processing\, process control and other areas of systems en gineering. This talk will give the flavour of this lesser-known aspect of Martin’s work. Foremost will be his Shifted Rayleigh Filter (SRF) for es timating the state of a moving target from noisy bearings-only measurement s (i.e. the direction cosines of the position of the target relative to th e sensor platform). The key idea behind his algorithm is that a small chan ge to the measurement model leads to simple\, exact formulae for the first and second order moments of the relevant conditional distributions. The S RF is superior\, in terms of accuracy and stability\, to traditional algor ithms based on the Extended Kalman Filter and its refinements. In the most challenging tracking scenarios where the EKF fails altogether\, the perfo rmance of the SRF is comparable to that of particle filters\, while reduci ng the computational demands by orders of magnitude. Other examples given of his work will include his elegant application of the work of Elliot/Kal ton\, linking risk averse formulations of optimal exit time problems for c ontrolled diffusions and differential games\, to practical problems of flo w control.\n\nSpeaker: Terry Lyons\nTitle: Beyond Diffusion: Clark’s 196 6 Thesis and the Path to Rough Models in Data Science\nAbstract: In his 19 66 thesis\, Clark approached stochastic systems from the perspective of ph ysically observed signals with short correlation times. He did not begin b y postulating Brownian motion. What emerges from his analysis is that conv ergence of the system dynamics depends not only on the limiting signal\, b ut also on additional second-order structure inherited from the noise. In modern language\, he identified the need for more than just the path—alt hough he encoded this structure statistically rather than pathwise. This v iewpoint feels very natural today\, especially in data-driven settings whe re signals are observed rather than assumed\, and where the higher-order s tructure captured by rough path theory is increasingly shaping the analysi s of sequential data.\n\nSpeaker: Nigel Newton\nTitle: Stochastic Calculus and Information Geometry in Nonequilibrium Statistical Mechanics\nAbstrac t: The Itô calculus is an ideal tool for the study of statistical mechani cal systems in continuous time.   The talk will illustrate its use in th e context of an electrical circuit containing Nyquist-Johnson resistors.    Temperature differences within the circuit lead to a nonequilibrium sta tionary state\, in which energy flows between two components.  This is as sociated with entropy production and a flow of Shannon information called the directed information.  The flows are connected by a mesoscopic varian t of the Second Law of Thermodynamics – regarding the donor of energy as a heat bath\, and the recipient as a Maxwellian demon having access to pa rtial observations\, the directed information quantifies the maximum rate at which the demon can extract ‘’work’’ from the heat bath.  This is achieved under constraints on the circuit parameters\, including an in equality constraint on temperatures and an equality constraint under which the demon implements a Kalman-Bucy filter.  The talk will discuss time-r eversal\, innovations and the thermodynamic cost of optimal filtering.  T he rates of entropy production and directed information are naturally expr essed in terms of quadratic variation processes on statistical manifolds\, as measured in the Fisher-Rao Riemannian metric.\nBased on joint work wit h: Henrik Sandberg (KTH)\, Jean-Charles Delvenne (Louvain-la-Neuve) and Sa njoy Mitter (MIT).\n\nSpeaker: Eugene Wong\nTitle: Conditional Expectation and Generative AI: Computing the Score Function                                                              \nAbstract: Conditional expectation and machine learnin g can be used to deal with the same problem\, namely\, regression. As capa bility for computation advanced\, machine learning has become the unchalle nged champion for solving data driven regression. Its scalability to large data vectors\, ability to accommodate vast training sets\, independence f rom mathematical models\, and above all\, a remarkable ability for general ization\, have made it the foundation for the AI revolution that is sweepi ng the world economy. However\, as the proliferation of data centers attes ts\, machine learning has an insatiable appetite for computation\, in both capacity and time.  \nGenerative AI deals with the following problem: Gi ven a collection of objects of the same type (e.g.\, images\, texts)\, we want to generate new and interesting examples of the same type. The new ex amples should look like they belong to the initial collection\, but not to o much like any one of them. A popular approach is the Diffusion Model: In this approach a diffusion equation is used to produce a large set of data samples from the starting examples. The data samples are then used in a m achine learning computation to produce a second diffusion equation which i s used to generate the new examples. In this talk we propose a way to repl ace the machine learning operation by a direct estimation of conditional e xpectation. In particular\, we try to identify the various functions that make machine learning so effective and replicate them in the conditional e xpectation approach. Our goal is to match or exceed the efficacy of machin e learning in Generative Ai\, and with much greater efficiency.\nIn this t alk\, we present a formulation of the generative AI problem as one of data -driven estimation of conditional expectation and some early evidence of i ts efficacy and computational efficiency.\n\nSpeaker: Malcolm Smith\nTitle : A Wiener spring theorem: the story of a collaboration with Martin Clark\ nAbstract: Numerical investigations carried out by my postdoc Stuart Swift in 2008 pointed towards a remarkable fact: that the mean power dissipated in a vehicle suspension was seemingly independent of suspension configura tion and parameters. In due course Stuart and I managed to prove that\, fo r a quarter-car vehicle model with a linear tyre spring\, the mean power d issipated in the suspension is equal to kA/2 where k is the tyre spring co nstant and A is the white noise intensity for the vertical road velocity f orcing.  The proof made use of Cauchy’s residue theorem to evaluate a f requency-domain formula for the mean power. A conversation with Martin at the Cancun CDC in December 2008 led to much rumination on his part\, and e ventually a beautiful proof of a more general version of the result using Ito calculus.  The process that turned Martin’s handwritten notes into a joint paper at the 2012 CDC in Maui will form part of the story in this talk and is almost as interesting as the proof itself.\n\nSpeaker: Peter E . Caines\nTitle: Mean Field Control and Games on Large Networks\n Abstrac t: Contemporary technological systems often have a network structure of bo th great scale and complexity\; examples are provided by the internet\, el ectrical power grids and air traffic systems. Furthermore\, the natural wo rld reveals a vast array of complex networks which includes the human micr obiome and the brain. All these networks support dynamical processes\, oft en with feedback loops which are inherent\, designed or a combination of b oth. \nIn this talk\, results on  Stochastic Control and Mean Field Gam es for large populations on large networks will be presented in terms of t he limits of sparse and dense networks\; these results include the existen ce and uniqueness of optima and Nash equilibria together with their approx imation to source problems with finite populations on finite networks.\n\n Speaker: Andrew Heunis\nTitle: Stochastic optimal control in mathematical finance\nAbstract: Mathematical finance has\, since its very inception\, b een much concerned with stochastic optimal control\, and continues to pres ent challenging control problems. These problems are typically of two vari eties\, namely utility maximisation and risk minimisation\, the latter pro blem involving in essence the minimisation of a mean-square criterion. Sta ndard methods of optimal control\, such as dynamic programming and the max imum principle\, do not apply very easily to these problems. On the other hand\, the problems enjoy the very nice special properties of being convex and having a single-dimensional state space. These properties are key to the application of a variational method\, due to Rockafellar and Moreau\, for addressing general mathematical programming problems for the minimisat ion of a scalar convex function defined on an abstract (typically infinite -dimensional) vector space. We shall briefly outline the variational metho d\, then illustrate application of the method to a succession of risk mini misation problems for which there are (a) no constraints\, (b) control con straints only\, and (c) a combination of control and almost-sure state con straints. The latter problem (c)\, which naturally leads to “singular” Lagrange multipliers\, seems to present some particularly interesting cha llenges.\n\nSpeaker: Thomas Cass\nTitle: Solving Signature Kernels as Two- Parameter Rough Differential Equations\nAbstract:  Signature kernels prov ide a principled way to compare sequential or streamed data by embedding p aths into a reproducing kernel Hilbert space by using their Chen–Fliess series (or signature transform). This embedding provides a way of enabling kernel methods to operate directly on path-valued data. They combine the expressive power of signature features with the scalability and universali ty of kernel methods.\nWe develop a two‑parameter rough path framework f or rough differential equations on rectangular and simplicial domains\, mo tivated by signature and Schwinger–Dyson kernel equations. Working in sp aces of jointly controlled rough paths\, we introduce a robust notion of t wo‑dimensional rough integration. Within this setting\, the signature ke rnel and the Schwinger–Dyson kernel are shown to arise naturally as solu tions of two‑parameter rough differential equations\, yielding well‑po sedness\, stability\, and principled numerical schemes with explicit compl exity guarantees.\nThis joint work with Andrea Iannucci\, Dan Crisan and W illiam F. Turner.\n\nSpeaker: Harry Zheng\nTitle: Duality Method for Multi dimensional Nonsmooth Constrained Linear Convex Stochastic Control\nAbstra ct: We discuss a general multidimensional linear convex stochastic control problem with a nondifferentiable objective function\, control constraints \, and random coefficients. We formulate an equivalent dual problem\, prov e the dual stochastic maximum principle and the relation of the optimal co ntrol\, optimal state\, and adjoint processes between primal and dual prob lems\, and illustrate the usefulness of the dual approach with some exampl es. (Joint work with Engel Dela Vega)\n\nSpeaker: Yufei Zhang\nTitle: Dete rministic Policy Gradient Methods in Continuous Time and Space\nAbstract:  The theory of continuous-time reinforcement learning (RL) has progressed rapidly in recent years. While the ultimate objective of RL is typically to learn deterministic control policies\, most existing continuous-time RL methods rely on stochastic policies. Such approaches often require sampli ng actions at very high frequencies\, and involve computationally expensiv e expectations over continuous action spaces\, resulting in high-variance gradient estimates and slow convergence.\nIn this paper\, we introduce det erministic policy gradient methods for continuous-time RL. We derive a con tinuous-time policy gradient formula expressed as the expected gradient of an advantage rate function and establish a martingale characterization fo r both the value function and the advantage rate. Building on this foundat ion\, we propose a model-free continuous-time Deep Deterministic Policy Gr adient (CT-DDPG) algorithm that enables stable learning for general reinfo rcement learning problems with continuous time-and-state. Numerical experi ments show that CT-DDPG achieves superior stability and faster convergence compared to existing stochastic-policy methods.\n\nSpeaker: Mihalis Zervo s\nTitle: A Dynamic Competitive Equilibrium Model of Irreversible Capacity Investment with Stochastic Demand and Heterogeneous Producers\nAbstract: We formulate a continuous-time competitive equilibrium model of irreversib le capacity investment in which a continuum of heterogeneous producers sup plies a single non-durable good subject to exogenous stochastic demand. Ea ch producer optimally adjusts both output and capacity over time in respon se to endogenous price signals\, while investment decisions are irreversib le. Market clearing holds continuously\, with prices evolving endogenously to balance aggregate supply and demand through a constant-elasticity dema nd function driven by a stochastic base component. The model admits a mean -field interpretation\, as each producer’s decisions both influence and are influenced by the aggregate behaviour of all others. We show that the equilibrium price process can be expressed as a nonlinear functional of th e exogenous base demand\, leading to a three-dimensional singular stochast ic control problem for each producer. We derive an explicit solution to th e associated Hamilton-Jacobi-Bellman equation\, including a closed-form ch aracterisation of the free-boundary surface separating investment and wait ing regions.\n\nSpeaker: Dan Crisan\nTitle: The identification of diffusio ns from imperfect observations: Martin’s last “big sum”.\nAbstract: I will discuss the identification of a d-dimensional diffusion X when a ru nning function of it is observed. A point-wise observation of the process (in other words\, observing it in isolation) cannot identify unless the fu nction is injective. However observing it on a small interval can be enoug h to determine exactly. I will present results that expand on this idea\; in particular\, a property of ‘fine total asymmetry’ of twice continuo usly differentiable function is introduced that depends on the fine topolo gy of potential theory and that is both necessary and sufficient for X to be adapted to a natural right-continuous filtration generated by the obser vations. For real-analytic h the property reduces to simple asymmetry. A s econd result concerns the case where X is adapted to an augmented filtrati on generated by the observation process.\nThe talk is based on the paper M artin’s last paper:\nJMC Clark\, D Crisan\, The identification of diffus ions from imperfect observations\, Probability Theory and Related Fields\, 1-29\, November 2025. URL:https://www.imperial.ac.uk/events/207576/conference-in-honour-of-dr-mar tin-clark/ DTSTART;TZID=Europe/London:20260526T090000 DTEND;TZID=Europe/London:20260527T170000 LOCATION:tbc\, 170 Queens Gate\, South Kensington Campus\, Imperial College London\, London\, SW7 5HF\, United Kingdom END:VEVENT BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT DTSTART:20260526T090000 TZNAME:BST TZOFFSETTO:+0100 TZOFFSETFROM:+0100 END:DAYLIGHT END:VTIMEZONE END:VCALENDAR