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We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop…
We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
This paper has been withdrawn by the authors. We present a framework for sequential decision making in problems described by graphical models. The setting is given by dependent discrete random variables with associated costs or revenues. In…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator -- notably, as arising in the presence of external control. Our approach, which builds upon Krylov…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
This paper investigates the role of high-dimensional information sets in the context of Markov switching models with time varying transition probabilities. Markov switching models are commonly employed in empirical macroeconomic research…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a stochastic process with uncertain parameters. We develop a general framework which can be seen as a version of the martingale problem method…
We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the…
Modern approaches to causal modeling give a central role to interventions, which require the active input of an observer and introduces an explicit `causal arrow of time'. Causal models typically adopt a mechanistic interpretation,…
We study the structure of quantum Markov Processes from the point of view of product systems and their representations.
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We…