mathematics

Gisiro Maruyama

Gisiro Maruyama is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gisiro Maruyama rather than just read about it. In short: Gisiro Maruyama (丸山儀四郎, Maruyama Gishirō; April 4, 1916 – July 5, 1986) was a Japanese mathematician, noted for his contributions to the study of stochastic processes. The Euler–Maruyama method for the numerical solution of stochastic differential equations bears his name.

Key takeaways

Gisiro Maruyama belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Gisiro Maruyama to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Gisiro Maruyama from memory before moving on to harder problems.

Reference excerpt

Gisiro Maruyama (丸山儀四郎, Maruyama Gishirō; April 4, 1916 – July 5, 1986) was a Japanese mathematician, noted for his contributions to the study of stochastic processes. The Euler–Maruyama method for the numerical solution of stochastic differential equations bears his name. Maruyama was born in 1916 and graduated from Tohoku University, where he studied Fourier analysis and physics. He began his mathematical work with a paper on Fourier analysis in 1939. He became interested in probability theory through the study of Norbert Wiener's work. He was appointed Assistant professor at the Kyushu University in 1941. When Kiyosi Itô published his papers on stochastic differential equations in 1942, Maruyama immediately recognized the importance of this work and soon published a series of papers on stochastic differential equations and Markov processes. Maruyama is known in particular for his 1955 study of the convergence properties of the finite-difference approximations for the numerical solution of stochastic differential equations, now known as the Euler–Maruyama method. In harmonic analysis, he studied the ergodicity and mixing properties of stationary stochastic processes in terms of their spectral properties. Maruyama also studied quasi-invariance properties of the Wiener measure, extending previous work by Cameron and Martin to diffusion processes.

References

External links Gisiro Maruyama / Eugene B. Dynkin Collection of Mathematic Interviews / Cornell University Library

Illustrations

Gisiro Maruyama: Gisiro Maruyama — Gisiro Maruyama

Worked examples

Example 1 — a first encounter with Gisiro Maruyama

Start with the simplest possible case. Write down what Gisiro Maruyama claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gisiro Maruyama before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Gisiro Maruyama ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Gisiro Maruyama

In research: Gisiro Maruyama appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Gisiro Maruyama in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Gisiro Maruyama is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1916 births, 1986 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Gisiro Maruyama outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Gisiro Maruyama in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Gisiro Maruyama means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Gisiro Maruyama out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Gisiro Maruyama in simple terms?

Why does Gisiro Maruyama matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Gisiro Maruyama?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gisiro Maruyama.