A Generalization of Our Exit-problem for a Class of Non-Markov Processes With Path Dependency Paper

7 Mar 2025

In this section, we present the possible generalization of Assumptions A-1 and A-2 as well as the exit-time result for this more general process

Exit-Problem for a Class of Non-Markov Processes With Path Dependency: Proofs of Auxiliary Lemmas

6 Mar 2025

We take a closer look at our proofs of Auxiliary Lemmas.

Exit-Problem for a Class of Non-Markov Processes With Path Dependency: Proof of the Main Theorem

6 Mar 2025

Given the results of Lemmas 3.2 and 3.5, we expect our process to spend most of its time near a with σ small enough.

Exit-Problem for a Class of Non-Markov Processes With Path Dependency: The Auxiliary Results

6 Mar 2025

The first result that we will use for proving the main theorem describes convergence of the solution to the system.

Exit-Problem for a Class of Non-Markov Processes With Path Dependency: A Peek at the Exit-Time

6 Mar 2025

First, we present the following assumptions on domain G and geometry of the potentials that drive the system inside the domain.

The Compactness Results of Our Non-Markov Processes With Path Dependency Paper

6 Mar 2025

Let us present two results about the compactness of some sets that will be used later in the proof.

Results Related to the LDP: An Explanation

5 Mar 2025

The following lemma generalizes the large deviation principle for the case of converging initial conditions.

Establishing the LDP for the SID: What Does It Mean?

5 Mar 2025

In this section, we prove LDP for Self-Interacting diffusions of the type (1.7). First, we introduce the following group of main assumptions.

A Quick Explanation of the Large Deviation Principle

5 Mar 2025

In this paper, Large Deviations techniques are widely used. Here, by the Large Deviation Principle (LDP) we mean the following asymptotic behavior of measures.