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The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
This paper is devoted to the study of the large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. This work is the sequel of [13] in which a probabilistic method was developped to show that the…
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are…
We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
We investigate discrete-time mean-variance portfolio selection problems viewed as a Markov decision process. We transform the problems into a new model with deterministic transition function for which the Bellman optimality equation holds.…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…
We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic…
Advanced measurement techniques and high performance computing have made large data sets available for a wide range of turbulent flows that arise in engineering applications. Drawing on this abundance of data, dynamical models can be…
This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
We establish the existence of solutions to common noise McKean-Vlasov martingale problems for coefficients with low regularity. Our approach is able to handle the key challenge posed by drift coefficients that are discontinuous with respect…
This paper studies discrete-time two-person nonzero-sum linear quadratic stochastic games with random coefficients. Using convex variational analysis, we derive necessary and sufficient conditions for the existence of open-loop Nash…
We study discretizations of fractional fully nonlinear equations by powers of discrete Laplacians. Our problems are parabolic and of order $\sigma\in(0,2)$ since they involve fractional Laplace operators $(-\Delta)^{\sigma/2}$. They arise…
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the…
In this paper, we study the relationship between general maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems, where the control domain is not necessarily convex. The original problem is…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
We study the backward Kolmogorov equation on the space of probability measures associated to the Kushner-Stratonovich equation of nonlinear filtering. We prove existence and uniqueness in the viscosity sense and, in particular, we provide a…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…