We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of nonlinear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exists a critical noise value that separates regimes where optimal control yields qualitati...

For a given stochastic process X, its segment Xt at time t represents the “slice” of each path of X over a fixed time-interval [t−r, t], where r is the length of the “memory” of the process. Segment processes are important in the study of stochastic systems with memory (stochastic functional differential equations, SFDEs). The main objective of this paper is to study non-linear transforms of se...

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward extension of the real-valued situation. We apply this definition to introduce a stochastic integral with respect to cylindrical Wiener processes. Again, this defin...

Let W denote a standard Wiener process with W0 = 0. For a variety of reasons, it is desirable to have a notion of an integral ∫ 1 0 HsdWs, where H is a stochastic process; or more generally an indefinite integral ∫ t 0 HsdWs, 0 ≤ t < ∞. If H is a process with continuous paths, an obvious way to define a stochastic integral is by a limit of sums: let πn[0, t] be a sequence of partitions of [0, t...

Abstract. Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in t...

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...

We associate with a stochastic cocycle Θ = (φ,Φ), on Y = Ω×H, a stochastic variational integral equation and we characterize the exponential instability in mean square of stochastic equations in therms of solvability of the associated equation. Thus we obtain a generalization of stochastic case for results obtained by O. Perron [8], in deterministic case. 2000Mathematics Subject Classification:...

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted Msolutions is established. Two duality principles between linear mean-field (forward) stochastic Volterra integral equations (MF-FSVIEs, for short) and MF-BSVIEs are obtained. Several comparison theorems for MF-FSVIEs and MF...

When a random field (Xt, t ∈ R2) is thresholded on a given level u, the excursion set is given by its indicator 1[u,∞)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to...