Definition and Scope of Stochastic Quantization

Definitions and mathematical statement

The supplied record asks, "What is stochastic quantisation?" It supplies neither a mathematical definition to formalize nor a conjecture with a determinate conclusion. Its accompanying discussion concerns the scope of stochastic analysis, mentioning stochastic integration, Itô's formulas, and the existence, conditioning, uniqueness, and convergence of diffusion processes. These topics are contextual examples, not specified hypotheses or conclusions.

The supplied source-verification annotation characterizes the question as the rhetorical title of an expository discussion and marks the statement as unrecoverable. The extracted text ends mid-sentence. No state space, stochastic evolution, target probability measure, parameters, boundary conditions, or quantified property is specified. Consequently, no precise mathematical assertion about stochastic quantisation can be recovered from this record without adding unsupported choices. A definition through a particular stochastic dynamics or invariant measure would be an additional interpretation, not a statement supplied by this record.

The registry label open is supplied curation and does not establish that this rhetorical question constitutes an open mathematical problem. The supplied literature assessment says that the method and rigorous examples are established, while the extracted record specifies no single claim to classify as solved. That assessment is retained as supplied context, not independently verified mathematics.

Short English statement

The record asks for an explanation of stochastic quantisation, but its incomplete expository excerpt specifies no mathematical problem with a definite target. A precise theorem or conjecture cannot be extracted without further source material. The supplied open label and literature assessment remain unverified registry annotations.

Sources

• Local UnsolvedMath registry, permanent ID 30005138, source problem code catalogue entry, title "Definition and Scope of Stochastic Quantization." The supplied record has no named proposer, no clean statement, and statement status unrecoverable.
• Supplied report citation: Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, pp. 1501--1550, DOI 10.4171/owr/2022/27. https://doi.org/10.4171/owr/2022/27. The background describes Oberwolfach Reports as documenting workshops and their open-problem discussions. The supplied verification annotation says that this particular title introduces an expository discussion rather than a determinate mathematical question; that annotation has not been independently checked.
• Supplied literature source labeled "Namiki, stochastic quantisation": https://doi.org/10.1143/PTPS.111.1. No fuller bibliographic information is supplied.
• Supplied literature source labeled "Oberwolfach report": https://doi.org/10.4171/owr/2022/27.
• Literature assessment checked at 2026-08-22: supplied status open. The supplied assessment describes an established method with rigorous examples but no single extracted mathematical claim to mark solved. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment; its time-sensitive status and cited claims require independent verification.
• The excerpt attributes a discussion of the difficulty of defining stochastic analysis to D. Stroock, reference [16], and a historical account connecting Itô's calculus with Feller's theory of diffusions to Stroock, reference [15]. Neither reference is bibliographically identified in the supplied record, and the historical sentence is truncated. These attributions are preserved as excerpt-level claims only.