Quasimartingale¶
An adapted stochastic process of finite mean variation; with càdlàg paths it coincides with a semimartingale.
Core Idea¶
A quasimartingale is an adapted integrable stochastic process with finite mean variation, defined as a supremum over partitions of conditional expected increments plus the terminal expectation.
Partition sums of conditional expected increments remain uniformly bounded. A càdlàg quasimartingale falls into the semimartingale class.
Scope of Application¶
- Stochastic processes. Classifies integrator-like processes.
- Semimartingale theory. Uses the càdlàg equivalence.
- Probability. Studies conditional variation.
- Finance. Clarifies admissible process classes.
Clarity¶
Include adapted integrable processes whose conditional mean-variation supremum is finite. Exclude finite pathwise variation alone, nonadapted processes, and semimartingale synonymy without a càdlàg convention. Inclusion test: Include adapted integrable processes whose conditional mean-variation supremum is finite. Exclusion test: Exclude finite pathwise variation alone, nonadapted processes, and semimartingale synonymy without a càdlàg convention. Nearest boundary: A semimartingale is a close neighbor; equivalence requires the path-regularity convention stated by the source. Exit condition: The class ends when mean variation diverges. Common misclassifications: It is not finite pathwise variation. It is not necessarily càdlàg. It is not nonadapted. It is not automatically a martingale. Nearest named distinctions: Martingale: Has zero conditional drift. Semimartingale: Coincides under càdlàg regularity. Finite-variation process: Uses pathwise variation. Submartingale: Has one-sided conditional drift.
Manages Complexity¶
The definition controls conditional drift, not total sample oscillation. Dropping càdlàg broadens the class.
Abstract Reasoning¶
- Filtered space — Supplies time-indexed information. No filtration means no conditional increments.
- Adapted process — Makes each value observable at its time. Anticipating values violate the definition.
- Partitions — Discretize time for variation sums. One partition cannot establish the supremum.
- Conditional increments — Measure predictable mean change. Raw path variation is different.
- Finite supremum — Defines quasimartingale status. Infinite mean variation fails.
- Càdlàg regularity — Connects to semimartingales. Without it the classes need not coincide.
Knowledge Transfer¶
Finite-mean-variation analysis transfers among filtered processes only with integrability, adaptation, and partition conventions fixed; semimartingale conclusions require the stated path regularity.
Relationships to Other Abstractions¶
Current abstraction Quasimartingale Domain-specific
Parents (1) — more general patterns this builds on
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Quasimartingale is a kind of Stochastic Process Prime
Quasimartingale is a strict kind of Stochastic Process: it is an adapted stochastic process satisfying finite mean variation.
Hierarchy path (1) — routes to 1 parentless root
- Quasimartingale → Stochastic Process
Neighborhood in Abstraction Space¶
Quasimartingale sits in a crowded region of the domain-specific corpus (40th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Market & Economic Indices (5 abstractions)
Nearest neighbors
- Concurrent Estimation — 0.88
- Etemadi's Inequality — 0.88
- First-Hitting-Time Model — 0.88
- Maximising measure — 0.87
- Probability Density Function — 0.87
Computed from structural-signature embeddings · 2026-10-08