Related papers: Nonlinear Continuous Semimartingales
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that…
Estimating the conditional quantile of the interested variable with respect to changes in the covariates is frequent in many economical applications as it can offer a comprehensive insight. In this paper, we propose a novel semiparametric…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
In this work, we establish pathwise functional It\^o formulas for non-smooth functionals of real-valued continuous semimartingales. Under finite $(p,q)$-variation regularity assumptions in the sense of two-dimensional Young integration…
This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the…
In this report, we develop a semistability analysis framework for nonlinear systems with bounded time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown…
For non-anticipative functionals, differentiable in Chitashvili's sense, the It\^o formula for cadlag semimartingales is proved. Relations between different notions of functional derivatives are established.
For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical…
The martingale comparison method is extended to derive comparison results for path-independent functions for general semimartingales. Our approach allows to dismiss with the Markovian assumption on one of the processes made in previous…
This paper shows how the theory of dynamic risk measures provides viscosity solutions to a family of second-order parabolic partial differential equations, even in the degenerate case. First, motivated by the martingale problem approach of…
The main objective of this paper and the accompanying one \cite{ETZ2} is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work \cite{EKTZ}, focused on the…
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued…
This article deals with the study of a non-local one-dimensional quasilinear problem with continuous forcing. We use a time-reparameterization to obtain a semilinear problem and study a more general equation using semigroup theory. The…
Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional…
In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with…
We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…
We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…